The Black-Litterman Portfolio Problem With GARCH Estimating Volatility

With the development of global capital market,investment portfolio optimization problem plays an important role in the field of investment.Investors optimize the allocation of the assets,to minimize the risk of portfolio in given expected income situation.The classical Markowitz mean-variance portfolio model has laid the foundation for the development of modern quantitative finance.However,a large number of empirical studies have found that there are many shortcomings in the mean-variance model in practical application.One of the most important point is that the mean-variance model is very sensitive to the input parameters,and the small change of the expected return rate may result in the larger fluctuation of the final configuration result.In order to estimate the expected return of the risky assets more effectively,Fisher Black and Robert Litterman put forward the model of Black-Litterman and subjective view of investors is introduced in the model,in fact,is the market equilibrium of the benefit of investors and the point of view of a weighted average,this treatment can indeed improve the performance of the Markowitz mean-variance model of portfolio investment.But in practical application process,Fisher Black and Robert Litterman in the original Black-Litterman model not give quantitative investors view specific process and this is making investors view the metric to be a difficult.Black-Litterman model practical application.In order to overcome this difficulty,this paper introduces the GARCH model,which is embedded into the Black-Litterman model.As an application,this paper considers the problem of Black-Litterman model with the value of risk,and compares the influence of the embedded GARCH model.Abundant numerical comparison shows that the GARCH model is embedded in the Black-Litterman model,which can improve the SHARP ratio of the investment portfolio,and obtain a better cumulative effect.This paper is mainly divided into the following five parts.Firstly,Introduction.This chapter firstly describes the background and significance of this research,and then introduces the Black-Litterman model of the domestic and foreign research status quo and a brief review of the research content,and finally pointed out the innovation and shortcomings of this paper.Secondly,Black-Litterman Portfolio Model.In this chapter,we introduce the common mean variance portfolio model and the mean-VaR portfolio model to draw the Black-Litterman model,and then introduce the core idea,the process of Black-Litterman model and the method of parameter estimation in the model.Thirdly,Black-Litterman Model Based on GARCH Volatility Estimation.This chapter describes how to use the GARCH model to derive the Black-Litterman model to estimate the parameters.GARCH model is used to obtain the viewpoint of the Black-Litterman model,the GARCH model is used to solve the problem of Black-Litterman model,which can solve the problem of how to quantify the investor's point of view in Black-Litterman model.Fourthly,Empirical Research.In this chapter,we use the data of domestic and international data to carry out a wealth of numerical experiments,the mean variance framework and the mean-VaR framework.By using the traditional parameter estimation method and the Black-Litterman model,the GARCH model is used to verify the performance of the Black-Litterman model.Fifty,Conclusions.Based on the foregoing analysis,this chapter concludes that the improvement of the investment portfolio model and the improvement of the investment portfolio parameter estimation can improve the performance of the portfolio,and the improvement of the parameters estimation is better than that of the portfolio optimization problem.